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Recently it was discovered that the ground state orbital angular momentum intwo-dimensional chiral superfluids with pairing symmetry $(p_x+ip_y)^\nu$depends on the winding number $\nu$ in a striking manner. The ground statevalue for the $\nu=1$ case is $L_z=\hbar N/2$ as expected by counting theCooper pairs, while a dramatic cancellation takes place for $\nu>1$. The originof the cancellation is associated with the topological edge states that appearin a finite geometry and give rise to a spectral asymmetry. Here we study thereduction of orbital angular momentum for different potential profiles andpairing strengths, showing that the result $L_z=\hbar N/2$ is robust for$\nu=1$ under all studied circumstances. We study how angular momentum dependson the gap size $\Delta/E_F$ and obtain the result $L_z=\frac{\hbar\nu}{2}N(1-\frac{\mu}{E_F})$ for $\nu=2,3$. Thus, the gap-dependence of $L_z$ for$\nu<4$ enters at most through the chemical potential while $\nu\geq4$ isqualitatively different. In addition, we generalize the spectral asymmetryarguments to \emph{total} angular momentum in the ground state of tripletsuperfluids where due to a spin-orbit coupling $L_z$ is not a good quantumnumber. We find that the ground state total angular momentum also behaves verydifferently depending on total angular momentum of the Cooper pairs.

Ground state angular momentum, spectral asymmetry, and topology in chiral superfluids and superconductors